Decentralized channel assignment schemes are proposed to obtain low system-wide spatial overlap regions in wireless local area networks (WLANs). The important point of channel assignment in WLANs is selecting channels with fewer contending stations rather than mitigating interference power due to its medium access control mechanism. This paper designs two potential game-based channel selection schemes, basically each access point (AP) selects a channel with smaller spatial overlaps with other APs. Owing to the property of potential games, each decentralized channel assignment is guaranteed to converge to a Nash equilibrium. In order that each AP selects a channel with smaller overlaps, two metrics are proposed: general overlap-based scheme yields the largest overlap reduction if a sufficient number of stations (STAs) to detect overlaps are available; whereas decomposed overlap-based scheme need not require such STAs, while the performance would be degraded due to the shadowing effect. In addition, the system-wide overlap area is analytically shown to be upper bounded by the negative potential functions, which derives the condition that local overlap reduction by each AP leads to system-wide overlap reduction. The simulation results confirm that the proposed schemes perform better reductions in the system-wide overlap area compared to the conventional interference power-based scheme under the spatially correlated shadowing effect. The experimental results demonstrate that the channel assignment dynamics converge to stable equilibria even in a real environment, particularly when uncontrollable APs exist.